A Simple Graphics Program - Essentials of Interactive Computer Graphics - page 69

3.1 Coordinate Positions and Vertices

Poi n t (x 1 ,y 1 )

y -axis

x 1

From our experience developing computer programs, we understand that we must
somehow translate the measurements of Figure 3.2 into uniquely identifiable posi-
tions. Recall that the Cartesian coordinate system, with the origin and perpendic-
ular axes measuring distances, is a convenient tool to uniquely identify positions
in space. As illustrated in Figure 3.3, by the convention in 2D space, the upward

y 1

x -axis

Origin (0,0)

direction is associated with the y -axis, the rightward direction is associated with
the x -axis. We understand that the origin is located at the lower-left corner where
the lines x

Figure 3.3. The con-
vention for a 2D coordinate
system.

0 intersect.
Figure 3.4 shows that we can overlay the 2D cartesian coordinate system over
our paper, where we make choices about the following.

= 0and y =

• The origin. This is the reference position. In this case, a convenient

location for the origin is the lower-left corner of the paper.

( 0 , 0 )

• The axes. The choice of the origin and the Cartesian coordinate convention
dictate that the x -and y -axes should follow the paper's edges, where the x -
axis extends to the right and y -axis extends away.

Figure 3.4. Coordinate system and vertex positions.